Equivalently, \(bt(G)\)  is the least number of colors
which suffice to color the edges of \(G\)  so that no two edges of the same color
intersect other than at a common endpoint when the vertices of \(G\)  are arranged
in order around the boundary of a circle and the edges are drawn as straightline segments, minimized over all possible cyclic orderings of the vertices [3].
It is easy to see that \(G\)  has book thickness 1 if and only if \(G\)  is outerplanar
and \(bt(G) \le 2\)  if and only if \(G\)  is a subgraph of a planar Hamiltonian graph
[1]}.
